Continuous Time Extraction of a Nonstationary Signal with
Illustrations in Continuous Low-pass and Band-pass Filtering

Tucker McElroy and Thomas Trimbur

ABSTRACT

This paper sets out the theoretical foundations for continuous-time signal extraction in econometrics.
Continuous-time modeling gives an effective strategy for treating stock and flow
data, irregularly spaced data, and changing frequency of
observation.

We rigorously derive the optimal continuous-lag filter when the signal component is
nonstationary, and provide several illustrations,
including a new class of continuous-lag Butterworth filters for trend and cycle estimation.

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